1. Field of the Invention
The present invention relates to a wavetable synthesizer for usage in an electronic musical instrument. More specifically, the present invention relates to a digital reverberation simulator and operating method having a reduced memory size through usage of a decimation and interpolation filters.
2. Description of the Related Art
A synthesizer is an electronic musical instrument which produces sound by generating an electrical waveform and controlling, in real-time, various parameters of sound including frequency, timbre, amplitude and duration. A sound is generated by one or more oscillators which produce a waveform of a desired shape.
Acoustical characteristics of musical venues, including the finest concert halls and auditoriums, is highly dependent on reverberation characteristics. Synthesizers commonly use different forms of special effects to produce a pleasing sound. One highly pleasing special effect is reverberation simulation.
The first electronic reverberation simulators were designed using conventional analog circuitry. Analog reverberators were so difficult to design that designers commonly resorted to reverberation using mechanical devices such as springs and special metal plates.
Development of digital circuitry greatly eased the problems in producing reverberation simulators. Digital reverberators are highly flexible and produce nearly any imaginable form of reverberation. A simple digital reverberator includes a delay element and a mixer for mixing delayed and undelayed sound signals, thereby generating a single echo. Multiple echoes are simulated in a digital reverberator by feeding a portion of the delayed output signal back to the input of the delay element, creating a sequence of echoes. Reverberation parameters for an echo include the duration of the delay and the relative amplitudes of the delayed and undelayed sounds.
One parameter of the digital reverberator is a feedback factor F which is indicative of the strength of the signal fed back to the delay element. The feedback factor F has a value in the range from 0 to 1. The larger the feedback factor F, the longer the sequence of audible echoes. An advantage of digital reverberators over analog reverberators is that no signal fidelity is lost during multiple passes through the delay element so that a feedback factor F close to one as possible without a minor amplitude response peak exceeding unity feedback and causing oscillation.
However, even with a perfect delay line, a sequence of echoes at equal intervals does not produce a concert hall-type reverberation. The reverberation heard in a concert hall results from an inverse exponential decay of echo amplitude over time that is common in physical processes. The rate of decrease in echo signal amplitude is commonly expressed as the time for a 60-dB reduction in echo amplitude where the 60-dB level approximates the level at which the reverberation signal becomes inaudible. Typical concert hall reverberation times range from approximately 1.5 to 3.0 seconds.
A reverberation process is also characterized by an echo density parameter. A reverberator formed from a single delay line suffers from a low and constant echo density of about 0.03 echoes/msec. In contrast, a concert hall reverberation has an echo density which rapidly builds to that no echoes are distinguished. One measure of the quality of simulated reverberation is the interval between an initial signal and the time the echo density reaches 1 echo per msec. A good quality reverberator reaches this echo density in about 100 msec. To avoid the perception of a distant sound, a delay of 10 msec to 20 msec should be interposed between the initial signal and the first echo.
A reverberation process naturally has an uneven amplitude response which rises and falls with a periodicity equal to the reciprocal of the delay time. The uneven amplitude response of a concert hall-quality reverberation has peaks and valleys that are closely spaced, irregular, and moderate in height and depth. Commonly, concert hall reverberation has several peaks and valleys per hertz unit of bandwidth with a typical excursion between a peak and valley of approximately 12 dB. When a resonance chamber is small, sounds are produced with a high echo density and a low resonance density since resonant modes spanning a large number of wavelengths of moderate frequency sound are precluded by the limited distances between reflective surfaces. The converse condition of high resonance density and low echo density is produced by a lengthy delay time in a feedback delay reverberator, creating a sound alien to a typical reverberation sound.
A concert hall quality reverberation may be reproduced exactly by recording an impulse response of a selected concert hall and applying a transversal filter technique to a sound to be reverberated. Typical reverberations times of 2 seconds require usage of a filter that is 50K to 100K samples long, a size that is clearly impractical for implementation in an integrated circuit. However, many circuits created from delay elements, summers and multipliers produce a reverberation echo so long as the circuit is stable and does not oscillate.
A practical integrated circuit implementation of a concert hall quality reverberation simulator commonly includes several delay elements having unequal delay lengths. The values of the plurality of delay lengths, for example the placement of taps in a single delay line, determines the quality of sound of the simulator. A highly pleasing sound is produced by placing the taps according to an approximately exponential distribution but also a distribution in which the taps are placed at prime number locations. This structure of a reverberation delay line creates a maximum rate of echo amplitude growth.
High-quality audio reproduction using synthesis such as wavetable audio synthesis is only achieved in a system which includes a large amount of memory, typically more than one megabyte, and which commonly includes more than one integrated circuit chip. Such a high-quality wavetable synthesis system is cost-prohibitive in the fields of consumer electronics, consumer multimedia computer systems, game boxes, low-cost musical instruments and MIDI sound modules.
Implementation of reverberation simulation to greatly improve the quality of sound produced by a synthesizer substantially increases the size of volatile or buffer storage. For example, a synthesizer which generates a 16-bit digital audio stream at 44.1 kHz typically employs a delay buffer size of about 32 Kbytes, an amount far higher than is feasible for implementation in low-cost and single-chip environments.
What is needed is a reverberation simulator having a substantially reduced memory size and computational load, and a reduced cost while attaining an excellent audio fidelity.